tests/Pow_of_Matrix.test.cpp

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Last update: 2025-11-28 02:09:51+07:00
Problem: https://judge.yosupo.jp/problem/pow_of_matrix

Depends on

Code

#define PROBLEM "https://judge.yosupo.jp/problem/pow_of_matrix"

#include "../misc/macros.h"
#include "../math/ModInt.h"
#include "../math/Matrix.h"

using Fp = modint<998244353>;

void solve() {
  int n;
  u64 k;
  cin >> n >> k;
  Matrix<Fp> a(n);
  for (int i = 0; i < n; ++i)
    for (int j = 0; j < n; ++j) cin >> a[i][j];
  a = a.pow(k);
  for (int i = 0; i < n; ++i)
    for (int j = 0; j < n; ++j) cout << a[i][j] << " \n"[j + 1 == n];
}

int main() {
  cin.tie(0)->sync_with_stdio(0);
  cin.exceptions(cin.failbit);
  int tc = 1;
  // cin >> tc;
  for (int i = 1; i <= tc; ++i) {
    solve();
  }
}

#line 1 "tests/Pow_of_Matrix.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/pow_of_matrix"

#line 1 "misc/macros.h"
// #pragma GCC optimize("Ofast,unroll-loops")       // unroll long, simple loops
// #pragma GCC target("avx2,fma")                   // vectorizing code
// #pragma GCC target("lzcnt,popcnt,abm,bmi,bmi2")  // for fast bitset operation

#include <bits/extc++.h>
#include <tr2/dynamic_bitset>

using namespace std;
using namespace __gnu_pbds;  // ordered_set, gp_hash_table
// using namespace __gnu_cxx; // rope

// for templates to work
#define all(x) (x).begin(), (x).end()
#define sz(x) (int) (x).size()
#define pb push_back
#define eb emplace_back
using i32 = int32_t;
using u32 = uint32_t;
using i64 = int64_t;
using u64 = uint64_t;
using i128 = __int128_t;
using u128 = __uint128_t;
using ld = long double;
using pii = pair<i32, i32>;
using vi = vector<i32>;

// fast map
const int RANDOM = chrono::high_resolution_clock::now().time_since_epoch().count();
struct chash {  // customize hash function for gp_hash_table
  int operator()(int x) const { return x ^ RANDOM; }
};
gp_hash_table<int, int, chash> table;

/* ordered set
    find_by_order(k): returns an iterator to the k-th element (0-based)
    order_of_key(k): returns the number of elements in the set that are strictly less than k
*/
template <class T>
using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;

/*  rope
    rope <int> cur = v.substr(l, r - l + 1);
    v.erase(l, r - l + 1);
    v.insert(v.mutable_begin(), cur);
*/
#line 2 "math/ModInt.h"

template <int mod>
struct modint {
  using M = modint;
  static_assert(mod > 0 && mod <= 2147483647);
  static constexpr int modulo = mod;
  static constexpr u32 r1 = []() {
    u32 r1 = mod;
    for (int i = 0; i < 5; ++i) r1 *= 2 - mod * r1;
    return -r1;
  }();
  static constexpr u32 r2 = -u64(mod) % mod;
  static u32 reduce(u64 x) {
    u32 y = u32(x) * r1, r = (x + u64(y) * mod) >> 32;
    return r >= mod ? r - mod : r;
  }
  u32 x;
  modint() : x(0) {}
  modint(i64 x) : x(reduce(u64(x % mod + mod) * r2)) {}
  M& operator+=(const M& a) {
    if ((x += a.x) >= mod) x -= mod;
    return *this;
  }
  M& operator-=(const M& a) {
    if ((x += mod - a.x) >= mod) x -= mod;
    return *this;
  }
  M& operator*=(const M& a) {
    x = reduce(u64(x) * a.x);
    return *this;
  }
  M& operator/=(const M& a) { return *this *= a.inv(); }
  M operator-() const { return M(0) - *this; }
  M operator+(const M& a) const { return M(*this) += a; }
  M operator-(const M& a) const { return M(*this) -= a; }
  M operator*(const M& a) const { return M(*this) *= a; }
  M operator/(const M& a) const { return M(*this) /= a; }
  bool operator==(const M& a) const { return x == a.x; }
  bool operator!=(const M& a) const { return x != a.x; }
  M pow(u64 k) const {
    M res(1), b = *this;
    while (k) {
      if (k & 1) res *= b;
      b *= b, k >>= 1;
    }
    return res;
  }
  M inv() const { return pow(mod - 2); }
  friend ostream& operator<<(ostream& os, const M& a) {
    return os << reduce(a.x);
  }
  friend istream& operator>>(istream& is, M& a) {
    i64 v;
    is >> v;
    a = M(v);
    return is;
  }
};

u64 modmul(u64 x, u64 y, u64 m) { return u128(x) * y % m; }
u64 modpow(u64 x, u64 k, u64 m) {
  u64 res = 1;
  while (k) {
    if (k & 1) res = modmul(res, x, m);
    x = modmul(x, x, m);
    k >>= 1;
  }
  return res;
}
#line 1 "math/Matrix.h"
template <class T>
struct Matrix {
  int r, c;
  vector<vector<T>> a;
  Matrix(int n) : Matrix(n, n) {}
  Matrix(int r, int c) : r(r), c(c), a(r, vector<T>(c, T(0))) {}
  Matrix(const vector<vector<T>>& v) : r(sz(v)), c(v.empty() ? 0 : sz(v[0])), a(v) {}
  vector<T>& operator[](int i) { return a[i]; }
  const vector<T>& operator[](int i) const { return a[i]; }
  static Matrix eye(int n) {
    Matrix res(n);
    for (int i = 0; i < n; ++i) res[i][i] = 1;
    return res;
  }
  Matrix operator*(const Matrix& b) const {
    Matrix res(r, b.c);
    for (int i = 0; i < r; ++i)
      for (int k = 0; k < c; ++k)
        if (a[i][k] != T(0))
          for (int j = 0; j < b.c; ++j) res[i][j] += a[i][k] * b[k][j];
    return res;
  }
  Matrix pow(u64 k) const {
    Matrix res = eye(r), b = *this;
    while (k) {
      if (k & 1) res = res * b;
      b = b * b, k >>= 1;
    }
    return res;
  }
  // destructive
  pair<T, int> gauss() {
    int rank = 0;
    T det = 1;
    for (int j = 0; j < c && rank < r; ++j) {
      int k = rank;
      while (k < r && a[k][j] == T(0)) k++;
      if (k == r) {
        det = 0;
        continue;
      }
      swap(a[rank], a[k]);
      if (rank != k) det = -det;
      det *= a[rank][j];
      T inv = T(1) / a[rank][j];
      for (int l = j; l < c; ++l) a[rank][l] *= inv;
      for (int i = 0; i < r; ++i)
        if (i != rank && a[i][j] != T(0)) {
          T fac = a[i][j];
          for (int l = j; l < c; ++l) a[i][l] -= a[rank][l] * fac;
        }
      rank++;
    }
    return {det, rank};
  }
  pair<vector<T>, vector<vector<T>>> solve(const Matrix& b) const {
    if (r != b.r || b.c != 1) return {{}, {}};
    Matrix mat(r, c + 1);
    for (int i = 0; i < r; ++i) {
      for (int j = 0; j < c; ++j) mat[i][j] = a[i][j];
      mat[i][c] = b[i][0];
    }
    int rank = mat.gauss().second;
    vector<T> sol(c, T(0));
    vector<int> piv;
    vector<bool> is_free(c, 1);
    for (int i = 0; i < rank; ++i) {
      int j = 0;
      while (j <= c && mat[i][j] == T(0)) j++;
      if (j == c) return {{}, {}};
      piv.push_back(j);
      is_free[j] = 0;
      sol[j] = mat[i][c];
    }
    for (int i = rank; i < r; ++i)
      if (mat[i][c] != T(0)) return {{}, {}};
    vector<vector<T>> ker;
    for (int j = 0; j < c; ++j) {
      if (is_free[j]) {
        vector<T> v(c, T(0));
        v[j] = T(1);
        for (int i = 0; i < sz(piv); ++i) v[piv[i]] = T(0) - mat[i][j];
        ker.push_back(v);
      }
    }
    return {sol, ker};
  }
  T det() const {
    if (r != c) return T(0);
    Matrix tmp = *this;
    auto [d, rank] = tmp.gauss();
    return (rank == r) ? d : T(0);
  }
  int rank() const {
    Matrix tmp = *this;
    return tmp.gauss().second;
  }
  Matrix inv() const {
    if (r != c) return Matrix(0, 0);
    Matrix tmp(r, 2 * c);
    for (int i = 0; i < r; ++i) {
      for (int j = 0; j < c; ++j) tmp[i][j] = a[i][j];
      tmp[i][i + c] = 1;
    }
    auto [d, rank] = tmp.gauss();
    if (rank != r) return Matrix(0, 0);
    Matrix res(r, c);
    for (int i = 0; i < r; ++i)
      for (int j = 0; j < c; ++j) res[i][j] = tmp[i][j + c];
    return res;
  }
};
#line 6 "tests/Pow_of_Matrix.test.cpp"

using Fp = modint<998244353>;

void solve() {
  int n;
  u64 k;
  cin >> n >> k;
  Matrix<Fp> a(n);
  for (int i = 0; i < n; ++i)
    for (int j = 0; j < n; ++j) cin >> a[i][j];
  a = a.pow(k);
  for (int i = 0; i < n; ++i)
    for (int j = 0; j < n; ++j) cout << a[i][j] << " \n"[j + 1 == n];
}

int main() {
  cin.tie(0)->sync_with_stdio(0);
  cin.exceptions(cin.failbit);
  int tc = 1;
  // cin >> tc;
  for (int i = 1; i <= tc; ++i) {
    solve();
  }
}